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The club's all time top scorer has been under pressure in recent weeks as the Blues' have fallen to ninth in the table, and following the loss to Leicester City last weekend he became favourite to lose his job next.
Chelsea beat Luton Town on Sunday afternoon but, according to the Telegraph, that hasn't been enough for him to save his job.
According to the report the announcement is expected later today, with players told not to report to the training ground until this afternoon.
Lampard took charge of Derby County in May 2018 and stayed one season with the Championship club, helping them get to the play-offs.
They famously beat Leeds United in the semi-finals, after the pairs rivalry was increased due to the Spygate incident with Marcelo Bielsa, but lost in the final.
That was enough to get him the job at Stamford Bridge, following the sacking of Maurizio Sarri, and the Italian's return to Serie A.
He was given the job at Chelsea during their transfer ban and wasn't able to sign anyone in his first summer at the club.
The former New York City midfielder was praised for his use of Chelsea's youngsters, something previous managers hadn't done.
Mason Mount and Tammy Abraham were particularly impressive as Lampard began life as a Premier League manager well.
He had a tough spell in the middle of the season but the Blues hung on to fourth spot on the final day of the season to qualify for the Champions League, though they lost the FA Cup final to Arsenal.
Lampard has been under pressure this season from the off, simply because the club invested over £200 million in the summer on talent.
Kai Havertz, Timo Werner, Ben Chilwell, Hakim Ziyech Edouard Mendy and Thiago Silva were all brought in to boost the side.
The west London side had a decent start to the season, losing only once in 11 games, against champions Liverpool, but they have since lost five of their last eight in the league, winning just twice.
Lampard was the 16th manager since Roman Abramovich bought the club in 2003, including caretaker and interim managers.